SOME have offered sexual favors. Others promise cases of booze.Some claim to be long-lost relatives or close friends of Mel Brooks or Nathan Lane or Matthew Broderick – or all three.

Others say they are trying to honor the last request of someone who is terminally ill.

There is nothing, it seems, that people won’t say or do to score tickets to “The Producers.”

Since the $10.5 million musical opened to rave reviews, everyone associated with it – from the producers and creators to the press agent and house manager – has been inundated with requests for seats.

“I have never seen demand like this before,” says Paul Libin, managing director of Jujamcyn Theaters, which owns the St. James, where “The Producers” is running.

“People I haven’t heard from in years are calling me up, looking for tickets. My line is: ‘Too bad you didn’t call me yesterday. I had two wonderful seats on the aisle, and I had to give them away to total strangers.'”

Jujamcyn, along with the producers, creators, designers and stars, has access to nearly 200 “house seats,” as they are called in the theater business, for every performance of “The Producers.” The St. James Theatre seats 1,600.

House seats are the best spots in the orchestra and are generally not available to the public. They are reserved for celebrities and other VIPS, as well as friends and relatives of people involved in the show.

In other words, you have to be very well-connected to get them.

But in the case of a super-hot show like “The Producers,” even being very well-connected doesn’t mean you’ll automatically get a pair.

“Everybody you can possibly think of has called for tickets,” says Tom Viertel, one of the show’s producers. “The problem is, there just ain’t enough tickets to go around.”

The house seat allotment for May is already gone, says Viertel.

“We opened the house seat book for June today, and I expect those tickets will be gone within 48 hours,” he said.

Libin says Jujamcyn Theaters gets more than 100 requests for house seats a day.

John Barlow, the show’s press agent, says his office gets over 50 calls a day.

William Ivey Long, who designed the show’s costumes, says he gets 10 calls a day from people looking for tickets.

“Friends of my cousins from North Carolina wanted four tickets for the Fourth of July,” says Long. “I don’t think so!”

Robert Morgan, Long’s assistant, spends at least an hour a day handling house seat requests. He says people have offered to send over cases of expensive liquor in exchange for tickets.

Such offers are rejected out of hand, says Long.

“That’s bribery, and we don’t take bribes.”

Many people are willing to play any card – or try to pluck any heartstring – they can to get into the show.

Jujamcyn Theaters got a call from a man who claimed his best friend was dying of cancer and wanted nothing more than to see “The Producers.”

Unable to verify the story, Jujamcyn did not honor the request.

The press office also received a “this-is-my-last-request” call, this one from a woman in Florida who claimed she needed two tickets on a Saturday for her sister, who was dying of cancer.

“How do you discern whether something like that is true or not?” asks Barlow. “We do our best to handle requests, but our job is to provide tickets to members of the press who are working on a story about the show.”

Sex is another lure.

A woman recently standing on line at the theater walked up to the treasurer of the box office and offered to perform a certain sex act on him if he would let her cut to the front of the line.